I'm obviously not sure what your daughter's situation is, and it sounds a bit more extreme than mine was, so take what I'm about to say not as advice but just as a different perspective.
When I was a kid, I hated the texture of most foods. They made me gag. It wasn't necessarily the taste, and I really did wish I could eat vegetables because I knew they were good for me. They even smelled and looked good. But I just couldn't get past the texture.
My pediatrician was "old school" and told my parents that I was just a picky eater and not to worry about it. Did I eat dairy? Fortified cereals? Eggs and meat? If so, I'd be fine. His point was that kids just need macronutrients, and the vitamins sprayed on cereal plus a daily supplement was more than enough.
Did I under eat as a result? Probably. Was I a little under weight? Yeah, but not dangerously. Honestly, it probably helped me long term because my weight has never been a problem as an adult. I'm also normal height.
So, did I have an eating disorder? I mean, in a way, maybe. But it was a reaction to a sensation. I didn't have any other reason past "it feels gross in my mouth." I'm not an expert, but doesn't disordered eating need to be accompanied by "wrong thinking?" I had no other cause or motivation for my picky eating.
> she seems physically healthy; she runs and plays and doesn't get hurt
Again, I'm not trying to give advice because I don't know the specifics, but maybe don't worry too much unless she is actually presenting as physically unhealthy. Like, unless blood work shows some nutritional deficiency that can't be corrected with a vitamin supplement.
> She has been seeing a therapist, but I wonder if she needs to see a different therapist
Again, I don't know your situation, so maybe she is seeing a therapist for other reasons - but I believe that being made to see a therapist as a kid for my picky eating would have made things worse, especially since I didn't have any other problems. It may have even made me believe I had other mental problems.
I just didn't like the texture of most foods. Even as a kid I realized how weird that was, and that I should be eating more foods. I just couldn't do it physically until I was older and outgrew it. Now I'm fine. I'm an adventurous eater. I eat anything and everything, and I'm quite healthy.
Side note, I have adult friends who I learned were even pickier eaters than me as kids and who never really grew out of it. They're all fine, if maybe a little underweight.
There's evidence suggesting that super restrictive diets can extend lifespan. Also, hey, some people are just a little bit eccentric and have weird eating habits. Maybe they don't need to be "fixed." ymmv.